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# Method to solve 3 spheres of dough problem

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 128
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 00:06
Is the proper method to solving this problem: (1) find the volume of each sphere (2) add the volumes of the three spheres (3) calculate the radius from the new total volume?

There are three spheres of dough with diameters of 2, 4, and 6 cm. If the three are combined into one large sphere, what is the radius of the large sphere?
Ms. Big Fat Panda
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Joined: 09 Jun 2010
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Concentration: General Management, Nonprofit
Re: Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 00:27
Yep! That'd work
Intern
Joined: 23 Oct 2010
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Re: Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 01:29
(2^3 + 3^3 + 6^3) = R^3

Don't know an easier way.

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Re: Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 01:51
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KUDOS
Expert's post
tonebeeze wrote:
Is the proper method to solving this problem: (1) find the volume of each sphere (2) add the volumes of the three spheres (3) calculate the radius from the new total volume?

There are three spheres of dough with diameters of 2, 4, and 6 cm. If the three are combined into one large sphere, what is the radius of the large sphere?

Yes, R^3=(2/2)^3+(4/2)^3+(6/2)^3:

$$volume_{sphere}=\frac{4}{3}\pi{r^3}$$;

$$volume \ of \ the \ large \ sphere=\frac{4}{3}\pi{1^3}+\frac{4}{3}\pi{2^3}+\frac{4}{3}\pi{3^3}=\frac{4}{3}\pi{(1^3+2^3+3^3)}$$;

$$volume \ of \ the \ large \ sphere=\frac{4}{3}\pi{(1^3+2^3+3^3)}=\frac{4}{3}\pi{R^3}$$ --> $$R^3=1^3+2^3+3^3=36$$.
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Re: Method to solve 3 spheres of dough problem   [#permalink] 30 Dec 2010, 01:51
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